Sentaurus Structure Editor
4. Generating Meshes

4.1 Overview
4.2 Defining Mesh Strategies in Regions
4.3 Defining Refinement Windows
4.4 Defining Mesh Strategies in Refinement Windows
4.5 Defining a Multibox Mesh Strategy in Refinement Windows
4.6 Using a Layered (Offsetting) Mesh
4.7 Saving the Model
4.8 Meshing the Device Structure
4.9 Assignment

Objectives

• To set up meshing strategies for 2D devices.

4.1 Overview

This section gives instructions on how to generate meshes in the device structure. Meshing generations are usually required before a semiconductor device can be numerically solved for its electrical properties.

In Sentaurus Structure Editor, the meshing generation process is performed in two steps. The first step defines the meshing strategy, which includes steps that define the maximum and minimum meshing sizes in each of the device dimensions as well as the meshing refinement strategies. The second step links the defined strategy from the first step to a specific target, which is, in general, a material, or a device region, or a user-defined evaluation window.

Note that different device regions have different roles in terms of determining the device performance, thereby the required meshing strategies for these regions are typically different.

4.2 Defining Mesh Strategies in Regions

To define a simple meshing strategy in a device region:

1. Mesh > Refinement Placement.
   The Refinement Specification dialog box is displayed. It includes two input files: The Refinement Definition group box includes fields for defining the meshing strategy and the Placement Type group box deals with the placement.

   

   Figure 1. Refinement Specification dialog box. (Click image for full-size view.)

2. Type PlaceRF.Epi in the Placement Name field.
3. In the Placement Type group box, select Region as the placement type, and then R.Siliconepi as the region name.
4. In the Refinement Definition group box, type RefDef.Epi in the Name field.
   Enter 0.1 for the Max Element Size in X Direction, 0.005 for the Min Element Size in X Direction, 0.0125 for the Max Element Size in Y Direction, and 0.005 for the Min Element Size in Y Direction.
5. Apart from the above mesh-spacing specifications, physical fields that are computed during a device solution also can be used as reference points for the meshing refinement.
6. Select DopingConcentration from the Refinement Functions list, and enter 1 as the criterion for the Value Difference.
7. Click Add.
8. Click Add Placement to place the meshing strategy in the selected region.
9. Click Close.

The corresponding Scheme commands are:

(sdedr:define-refinement-window "BaseLine.Source" 
  "Line" (position -0.8 0.0 0.0) (position -0.2 0.0 0.0))
(sdedr:define-refinement-window "BaseLine.Drain" 
  "Line" (position  0.2 0.0 0.0) (position  0.8 0.0 0.0))

4.3 Defining Refinement Windows

In Sentaurus Structure Editor, a meshing strategy can be restricted to only selected areas. The areas (refinement windows) must be defined first before a meshing strategy can be applied.

To define a refinement window that covers the entire device:

1. Mesh > Define Ref/Eval Window > Rectangle.
2. In the view window, draw a rectangular window covering the entire device.
3. Enter (-0.5 1.0) and (0.5 -0.2) for the First Vertex and Second Vertex in the displayed Exact Coordinates dialog box.
   
   

   Figure 2. Exact Coordinates dialog box.

4. Click OK, and enter the name RefWin.all for the refinement.
5. Repeat the steps to define another refinement window, which covers the channel region only. Use the coordinates (-0.1 0.0) and (0.1 0.1) and the name RefWin.Channel.

The corresponding Scheme commands are:

(sdedr:define-refinement-window "RefWin.all" 
  "Rectangle" (position -0.5 1.0 0.0) (position 0.5 -0.2 0.0))
(sdedr:define-refinement-window "RefWin.Channel" 
  "Rectangle" (position -0.1 0.0 0.0) (position 0.1  0.1 0.0)) 

4.4 Defining Mesh Strategies in Refinement Windows

When a refinement window has been defined, placing a meshing strategy in a refinement window is performed in the same way as placing a meshing strategy in a region.

The only difference is to select Ref/Eval as the Placement Type and then select the target refinement window as follows:

1. Mesh > Refinement Placement.
   The Refinement Specification dialog box is displayed.

   

   Figure 3. Refinement Specification dialog box. (Click image for full-size view.)

2. Type PlaceRF.all in the Placement Name field.
3. Select Ref/Win as the placement type and select RefWin.all from the list.
4. Type RefDef.all in the Name field of the Refinement Definition group box.
   Enter 0.25 for the Max Element Size in X Direction, 0.1 for the Min Element Size in X Direction, 0.25 for the Max Element Size in Y Direction, and 0.1 for the Min Element Size in Y Direction.
5. If there are any predefined entries in the Refinement Functions group box, delete them.
6. Click Add Placement.
7. Click Close.

The corresponding Scheme commands are:

(sdedr:define-refinement-size "RefDef.all" 0.25 0.1 0.25 0.1)
(sdedr:define-refinement-placement "PlaceRF.all" "RefDef.all" "RefWin.all") 

4.5 Defining a Multibox Mesh Strategy in Refinement Windows

In some applications, numeric analysis may require meshing strategies in which meshing-line densities are changed gradually. For example, in the channel of a MOS transistor, a mesh with a tight vertical grid spacing near the silicon–oxide interface, which is relaxed gradually towards the bulk, is best suited to resolve the steep carrier-distribution gradients in the inversion layer while keeping the problem at a minimum of CPU time.

Sentaurus Structure Editor supports another type of meshing strategy called the multibox refinement strategy.

To access the multibox refinement strategy:

1. Mesh > Multibox Placement.
   The Multibox Specification dialog box is displayed.
   
   

   Figure 4. Multibox Specification dialog box. (Click image for full-size view.)

   This dialog box differs from the Refinement Placement dialog box. In the Multibox Definition group box, there is the Ratio field. This parameter of Ratio controls how fast the mesh spacing increases from the minimum to maximum value.

   A ratio of 1 suppresses any mesh relaxation, and the minimum value is used throughout the multibox. A ratio of, for example, 1.35, means that if the smallest requested mesh spacing is 1 Å, the second mesh spacing is 1.35 Å, the third is 1.82 Å, and so on. However, the quatree/octree meshing algorithm does not produce exactly the requested mesh spacing due to other structural or numeric considerations.

2. Type PlaceMB.Channel in the Placement Name field.
3. In the Placement Type group box, select the refinement window RefWin.Channel from the list. The Ref/Win list includes all the refinement windows that have been previously defined.
4. In the Multibox Definition group box, enter MB.Channel in the Name field.
5. In the X and Y fields, enter the values for both the maximum and minimum grid spacing:
   Max X = 0.05, Max Y = 0.0125, Min X = 0.025, Min Y = 0.0001.
6. Enter 1.0 for the X Ratio and 1.35 for the Y Ratio.
7. Click Add Placement.
8. Click Close.

The corresponding Scheme commands are:

(sdedr:define-multibox-size "MB.Channel" 0.05 0.0125 0.025 1e-4 1 1.35)
(sdedr:define-multibox-placement "PlaceMB.Channel" 
  "MB.Channel" "RefWin.Channel")

Although a ratio of between 1 and 2 can be specified in the Multibox Specification dialog box, the internal algorithm can only increase the mesh spacing of adjacent mesh cells by a factor of two. Therefore, in the structure, a sequence of mesh cells of a fixed spacing can be seen followed by a set of mesh cells of double-spacing, where the requested mesh spacing becomes twice the initial mesh spacing. The sign of the ratio value determines at which side of the multibox the grading starts. A positive value means that the grading starts at the left or top side, and a negative value means the grading starts at the right or bottom side of the multibox.

4.6 Using a Layered (Offsetting) Mesh

In certain cases, you may want to build mesh with lines that run parallel to a certain interface. For example, if the channel of a MOS transistor is curved or if the channel is straight but not aligned to one of the primary axes, it is more beneficial to use a layered mesh. This will create mesh lines that conform to the boundary, thereby reducing the number of mesh nodes at the same mesh spacing.

Sentaurus Structure Editor supports this type of meshing strategy called offsetting.

To define an offsetting mesh:

1. Mesh > Noffset Parameters.
   The Noffset Block Browser is displayed, listing the currently defined offsetting specifications.
   
   

   Figure 5. Noffset Block Browser. (Click image for full-size view.)

2. Click New to display the Noffset Block dialog box where you set the new offsetting specification.
3. Click the Noffset Interface tab.
   
   

   Figure 6. Noffset Block dialog box showing Noffset Interface tab.

4. Select the Region option for the block type since you want to define an offsetting mesh between two regions.
5. Choose R.Box as the first region and R.Siliconepi as the second region.
   The order of regions is important since offsetting is performed only in the first region (R.Box here). If you want to have offsetting on both sides of the interface, you must specify a second offsetting specification with the order of regions reversed.
6. Enter 0.004 for hlocal. This is the mesh spacing for the first layer of the mesh at the interface.
7. Enter 1.5 for factor. This factor multiplies the mesh spacing at each subsequent layer. A factor of 1.0 means that the mesh spacing of each layer remains constant and this is not recommended. Values in the range 1.2 to 2.0 should be used.
8. Click New.
9. Click Close.

The corresponding Scheme commands are:

(sdenoffset:create-noffset-interface 
	"region" "R.Box" "R.Siliconepi"
	"hlocal" 0.004
	"factor" 1.5)

4.7 Saving the Model

To save the model with the name soifet, follow the instructions in Section 2.14 Saving the Model.

The saved files are soifet.sat, soifet.scm, soifet_msh.cmd, and soifet_bnd.tdr.

Click to view all the commands discussed in this section in the command file soifet_dvs.cmd.

4.8 Meshing the Device Structure

To this point, several meshing strategies have been defined and placed in various device regions (windows). To create the mesh in the device, a meshing engine must be called.

To call the meshing engine:

1. Mesh > Build Mesh.
   The Build Mesh dialog box is displayed.
   
   

   Figure 7. Build Mesh dialog box. (Click image for full-size view.)

2. Enter soifet in the Save Grid to File field.
3. Select SNMESH from the Meshing Engine group box.
4. Command-line options for the meshing engine can be specified. Leave them empty.
5. Select Tecplot SV as the mesh viewer.
6. Click Build Mesh.

The corresponding Scheme command for launching the meshing operation is:

(sde:build-mesh "snmesh" "-offset" "soifet_msh")

This command saves two files used by the meshing engine, namely, the mesh command file soifet_msh.cmd and the boundary representation soifet_bnd.tdr of the device.

Click to view the mesh command file soifet_msh.cmd.

The meshing engine generates one mesh file, soifet_msh.tdr, which can be loaded as an input file for Sentaurus Device simulations.

Figure 8 shows the device structure with its current meshing and doping conditions, viewed using Tecplot SV.

Figure 8. Two-dimensional SOI MOSFET with its current meshing and doping conditions.

Figure 9 shows a detailed view of the mesh near the source/channel junction region.

Figure 9. Mesh near the source/channel junction region.

Click to view all the commands discussed in this section in the command file soifet_dvs.cmd.

The complete project can be investigated from within Sentaurus Workbench in the directory Applications_Library/GettingStarted/sde/soifet.

4.9 Assignment

Define a meshing strategy for the SiGe HBT from Section 3.5 Assignment.

Figure 10. Two-dimensional SiGe HBT with its current meshing and doping conditions.

Click to view a solution of the command file sigehbt_dvs.cmd.

The complete project can be investigated from within Sentaurus Workbench in the directory Applications_Library/GettingStarted/sde/sigehbt.